House Republican moderates, finding themselves a minority in the new House majority, are not planning to dig in their heels to try to drag the Conference to the center over the next two years.

But they are hoping to build coalitions that can shape policy.

“I don’t expect our stance on issues is going to differ much from the Conference,” said Rep. Jo Ann Emerson (Mo.), co-chairwoman of the centrist Tuesday Group. “I think it’s all going to depend. We’re just so early in the process.”

The 43-member Tuesday Group has met twice so far this Congress and has no plans to come up with an agenda of its own. In many ways, the moderate lawmakers said, they are still trying to figure out how they will fit in with the new House majority.

One thing seems evident, however. The Tuesday Group won’t take a cue from its Democratic equivalent, the moderate Blue Dog Coalition, which spent much of the past two years objecting to its Democratic leadership’s top priorities and pushing the agenda to the middle. Tuesday Group members say they prefer to make changes on the margins and hope to serve as a balance to newly elected conservative tea party Members.

Emerson noted that the group benefits from counting as one of its members Rep. Greg Walden (Ore.), a close ally to Speaker John Boehner (Ohio) who led the GOP transition. Emerson said Walden serves as a liaison between the Tuesday Group and the leadership.

“I think that we are interested in talking with anybody about anything,” Emerson said. “And I think it’s too early to make any blanket statements.”

Brad Dayspring, a spokesman for Majority Leader Eric Cantor (R-Va.), said his boss is “in constant communications with all Members.”

Former Rep. Tom Davis (Va.), who leads the centrist Republican Main Street Partnership, gave House GOP leaders high marks for their outreach to their moderate flank, saying they “know what they’re doing in terms of building coalitions.”

“We have no complaints with leadership at this point in terms of where they are going,” Davis told reporters at an event last week. “Main Streeters and moderates are not asking for control. We’re just asking to be part of the team, part of the coalition.”

Democrats, adjusting to their return to the minority, have said they see opportunities to align with centrist Republicans in the new Congress. A top ally for the Democratic moderates, Minority Whip Steny Hoyer (D-Md.), said Monday that wants to meet with Emerson and Rep. Charlie Dent (R-Pa.), the other Tuesday Group co-chairman, after this week’s recess. Hoyer has already met with GOP leaders and said he hopes they will enable deal-making between GOP moderates and Democrats.

“I’m hopeful that I can be a bridge — and I believe I can — between ourselves and a group that I think we might be able to reach common ground and work on some issues” with, Hoyer said.

“It’s been difficult to get moderates to come along if their leadership is adamantly opposed, so I think it’s a two-step process,” he added.

Emerson said she has not sought meetings with Blue Dogs, and Rep. Steven LaTourette (R-Ohio) noted that previous attempts to work with that bloc didn’t go anywhere.

“We tried, when they were in the majority, and they weren’t so interested in working with us on some issues,” he said. “There may be a repeat of that to try and reach out, but it’s not a stated goal of the Tuesday Group to be the finger in the eye of the Republican leadership.”

But LaTourette said he wants GOP colleagues to avoid politicizing their fiscal agenda because it could ultimately hurt the party in the next elections.

“From my perspective, at our peril we deviate from that ‘We have to get spending under control’ message to again go out and target things like the National Endowment for the Arts and the Public Broadcasting Service,” he said. “I think everyone accepts that difficult spending decisions have to be made, [but] I don’t know if the independents are going to go along with us if for a little bit of money we ideologically target them. So that’s a good place where we can make something happen.”

LaTourette and Emerson both noted that many of the centrists hail from Midwest and Northeast states where the GOP made significant gains in the last elections but in past years suffered. The Tuesday Group has also expanded its ranks to more conservative Members over the years, and 17 of the group’s 43 members also belong to the conservative Republican Study Committee. Yet while Tuesday Group members boast their largest roster ever, the group still makes up less than one-fifth of the GOP Conference. By comparison, the RSC’s 174 members represent more than half of all House Republicans.

Unlike the Tuesday Group, the RSC unveiled a sweeping legislative agenda for the 112th Congress and has laid down its marker for spending cuts and the upcoming debate over the debt limit.